And welcome to high school [physics] explained today
I'd like to talk about
Nuclear Spin and net Spin
Now if you were to go [onto] [Youtube] or various websites and look up the concept of spin
Then you will discover that there are lots of explanations that are quite good
but if you don't have a basic understanding of quantum mechanics
You'll probably struggle to understand it and so what I would like to do is talk about Spin from a high school perspective
So I'm not going to go too much into quantum mechanics, but if you want to understand spin
Especially if you're doing medical physics and want to understand spin in the context of Mris and hopefully this video will help you
So let's start first of all you have two protons and a proton has a positive charge
Now we're going to see that a proton has a number of properties and one of those properties is a concept called
Spin now Spin is actually a historical term we know that it actually doesn't
Literally spin, but if you consider that it is a positive charge
Then if it's spinning it may Spin in that direction
now if you're familiar with electromagnetism, then you know that a spinning charge will develop a
Magnetic Field and that magnetic
Field can be determined using a [right-hand] [grouper] also as a result of this spin it produces a magnetic
[field] in such a way that it is actually
Pointing upwards so in other words this end here will be the north pole this end over the south pole and as a result it
produces a magnetic field that goes around like so
What we have is this mediconnect field and the arrow represents the direction of the Magnetic field through the proton and so?
We call this a magnetic moment
Now what can also happen of course is I have a proton here
You can also have a spin
But in this case it could be spinning in the opposite direction and as a result
similarly - [here] it will produce a magnetic moment that is in the opposite direction, so
[here] I have a proton that has a magnetic moment that is pointing up, and we call it a spin up and over here
we have a proton that has a magnetic moment that it's down and we call it a spin down and
suffice to say in quantum mechanics
we give this a value and so the spin up is given a value of 1/2 if it is spin up and
Negative 1/2 if it's a spin down we don't worry about the numbers that goes into quantum mechanics
And I want to spare you from that what about two neutrons now neutrons as you know have no charge
but again
And this shows you how spin actually isn't a correct term the fact is that that neutrons have Spin and so
We can have a neutron that has a spin up and a neutron that has a spin down
Now again as I said this cannot be explained by imagining this as a charge
but nonetheless
Protons and neutrons have what we call a property called spin
And it can be two types of Spin Spin up or spin down
Similarly the spin up has a value of 1/2 and the spin down as a value of a negative 1/2 and again
I'm not going to go into detail as to why it is 1/2 or negative 1/2 and you can explore it yourself
So what then will happen if we combine protons and neutrons together in atoms?
So this is nuclear Spin, but what about if we combine those protons and neutrons?
Now to help you understand this I want to briefly touch on the quantum mechanics only
enough to help us understand what's going [on] here as you know that in terms of
electrons, we know electrons exist in specific orbits or energy levels well the same thing is true in the
Nucleus
protons and neutrons exist in different
energy levels to
Represent this I've got this little staircase, so the base here is energy one energy level two three and four and five [now]
Why is this important well if we start thinking about protons and neutrons. They are in the
Nucleus they exist only in specific energy levels and only a certain number can fit in each energy level
So let's take an example. Let's say we have one proton. So now we have hydrogen hydrogen has a
nucleus of only one proton so it's nuclear spin actually ends up being its net Spin because net Spin is a
Total sum total of its spin
[now] what happens if I add another?
Proton to it now if I add another proton to it. You'll notice that the arrow is pointing down and let me explain. Why
the Pauli Exclusion principle says no to set of
fermions
Can have the same set [of] quantum numbers now let me borrow that down real into simple
You can't have two fundamental particles having exactly [the] [same] properties
Now I'm not going to get into the details
Why that is so but needless to say I have two protons that have the same charge?
[I] have two protons that have this sitting on the same energy level
Therefore I cannot have them spinning in the same way so in order for them to coexist on to this energy level
one has to have [a] spin up of 1/2 one has to have a spin down a value negative 1/2, so
Although they have lots of similar properties and least in terms of spin
They're in the opposite direction, but what happens here is is that their spins cancels out?
although we have a nuclear spin here of 1/2 and
a negative 1/2 over here that leads us into a net spin of
0
If I add another proton to it, so let's say again. I now have my proton here and
another proton here, [I]
Want to add another proton well this one can't exist in this level it has to go to the next level because it can't have
The same numbers so in other words if now I have three protons in my nucleus
That would be example lithium. We're ignoring the neutrons [you] can see what happens is these two cancel out?
We now have another proton here
It is not the same set of quantum numbers because it's now on energy level two and so it's net Spin in this case is
[1/2]
Because I have these two cancel out and have 1/2 left over, but let's consider neutrons now for a moment
so let's look at an example of
Deuterium now deuterium is
Hydrogen with an extra neutron so here's my hydrogen one single proton, and I need a neutron over here
And you'll notice that they [have] the same direction in terms of Spin, but that's allowed because [there] are different subatomic particles
So they're allowed to coexist together as a result
We have now a net spin of 1/2 for the proton and a half
for the neutron and that leads us to a concept of net Spin of [1]
So [deuteriums] nucleus has a net spin of 1 because the proton the neutron would come together
So let's say I want to build up
Helium so helium has two protons, so here we go
I have a proton number 1 and I have to have a proton number 2 that spins in the opposite Direction
I now can add a neutron and a neutron of course can be in the same energy level
Because it is a different fundamental particle
But now if I add a second and [neutron] it has to spin down because it's appearing up with the other
[Neutron] and so now I have two protons two neutrons and in this case of [course] I
Have helium and helium of course has the mass number of four and an atomic number of two
But if you notice if you sum those spins up the net Spin ends up equaling
Zero because these two cancel up to cancel out giving us a zero
So you can see as we start to add?
Protons and Neutrons together we will get different spin values
Depending on what cancels out and what does not cancel out, so let's go a little bit more complex
So let's have a look at another element and let's start with
looking at Carbon 13 as an example so carbon 13 has
13 Nucleons and six of those are protons and as you can think of that that means there are seven neutrons to add
So let's add our protons and neutrons to the ladder so let's start with the protons first
So here's proton number one and here's proton number two you notice that they come in pairs spin up and spin down and we keep
the process going now, we're going on to the next [energy] [level] and we keep going like so and
Now I have my number of protons correct
We now add the neutrons and again the same rules apply once we start adding neutrons to our nucleus
but they always go up in pairs because they then jump up different energy levels, and I'm almost finished here and
Finally we have a [situation] like this, so I have six protons and seven neutrons
What is it spin?
Well if you look carefully, you can clearly see that
Every pair here cancels out so as a result the net Spin is
Totally determined by this last remaining neutron and so the net spin
Is equal to [1/2]?
We've dealt with an example of a spin of 0 and we've dealt an example with a spin of a half and we've dealt
example of a spin of a whole number
so there are some basic rules to help you know very quickly what net Spin exists and
The rules are like this if a is even and zed is odd then the spin is a whole number
So think about it z is odd
so therefore
You're automatically going to have a half a spin left over a is even that means
Automatically the number of neutrons is also. Odd which means you're going to have 1/2 left over those two halves or
automatically mean you get a spin of
One so here we go these two cancel out these add up
We get a whole number [if] a is even and zed is even then
Clearly we've got an even number of protons an even number of neutrons and as a result the net Spin is
zero if a is odd
Then basically you can get two combinations
you either have an even number of protons and an oDd number of Neutrons or an
even number of Neutrons and an odd number of protons
What's left of course is that you get a spin of 1/2 in fact it is multiples of 1/2 again?
That is quantum mechanics when I'm going to go into the reasons
Why it can be 3 over 2 and 5 over 2 but needless to say?
You always get multiples [over] [half] if the mass number is odd
so that summarizes the concept of Nuclear Spin and
Net Spin, and that should give you enough scope to help you with understanding
the concept of Spin in the context of Mri
[I] hope that's helped you and thanks for watching [bye] [for] now. I
Hope you found that video useful and remember like share and subscribe
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I'm paul from High school physics explained. Bye for now